Chapter 8.5, Problem 53E

Reconsider the paint-drying problem discussed in Example 8.5. The hypotheses were H₀: μ = 75 versus H_a: μ < 75, with σ-assumed to have value 9.0. Consider the alternative value μ = 74, which in the context of the problem would presumably not be a practically significant departure from H₀.

1. a. For a level .01 test, compute β at this alternative for sample sizes n = 100, 900, and 2500.
2. b. If the observed value of $\bar{X}$ is $\bar{x}$ = 74, what can you say about the resulting P-value when n = 2500? Is the data statistically significant at any of the standard values of α?
3. c. Would you really want to use a sample size of 2500 along with a level .01 test (disregarding the cost of such an experiment)? Explain.